An air jump is when a player jumps while in the air. While double jumping is not possible, air jumping is very similar and can a achieve much of the same affect. If a player walks into the air (such as walking off the edge of a platform) without jumping, their "jump" can be used just as if they were on the ground, and their ability to jump is reset when they hit the ground just like normal. This can allow players to jump farther and higher than normal.
While performing an air jump, you may continue to change direction. This can be especially useful if you want to walk up stairs into the air, shoot someone, air jump, and then angle back onto the stairs.
It is also possible to perform an air jump with just one block. If a player is standing on a platform with a block one row above it with no blocks 2-3 rows above that, it is possible to use the upward velocity from walking onto that block to walk up into the air, and then jump achieving higher heights. For the to work, as soon as the player hits the block and start moving up, they need make sure nothing stops their momentum such as a wall or block above. If there is a wall next to the block, the key is to start moving the to opposite horizontal direction as soon as you start going up.